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Nonlinear Forecast Error Variance Decompositions: Shapley Shares, Generalized Shapley Shares, and the Role of Structural Interactions

Author

Listed:
  • Frédérqiue Bec
  • Heino Bohn Nielsen

    (CY Cergy Paris Université, THEMA)

Abstract

Forecast error variance decompositions (FEVDs) are widely used to assess the contribution of structural shocks in vector autoregressions. However, many variables of interest are nonlinear functions of underlying variables, rendering the standard linear FEVD incomplete. We develop a framework for variance decomposition of nonlinear forecast targets in terms of the Shapley value decomposition and compare it with more conventional approaches based on Taylor expansions. We illustrate that nonlinear interaction effects can account for components of forecast uncertainty that are not fully captured by Taylor approximations. As a result, approximation-based FEVD may substantially distort the picture of forecast uncertainty and the attribution of variance across shocks.

Suggested Citation

  • Frédérqiue Bec & Heino Bohn Nielsen, 2026. "Nonlinear Forecast Error Variance Decompositions: Shapley Shares, Generalized Shapley Shares, and the Role of Structural Interactions," Thema Working Papers 2026-09, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    • Handle: RePEc:ema:worpap:2026-09
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    References listed on IDEAS

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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